The present invention relates to apparatus and method for measuring displacement for measuring the displacement amount of a surface of a measuring object without contact by scanning an irradiation point formed by light radiated onto the surface of the measuring object at a fixed interval utilizing triangulation by light. Particularly, the present invention relates to apparatus and method for measuring displacement for enhancing displacement detection precision and a measurement rate using a lens array. The present invention also relates to apparatus and method for measuring displacement that enable precisely acquiring the amount of displacement by correcting an error due to the dispersion of a position and a direction in which a lens array is installed and the focal length.
In case the displacement (irregularities) in the height of a surface of a measuring object is (are) measured using light, an apparatus for measuring displacement depending upon triangulation is used. In the apparatus for measuring displacement, a laser beam is radiated on the surface of a measuring object 52 from a projector 51 as shown in FIG. 20 and an image K at an irradiation point P is imaged on the light receiving plane of a light receiving element 54 through an imaging lens 53.
This light receiving element 54 outputs a signal corresponding to the amount of displacement in which an image formation point on the light receiving plane moves from the position of K to K′ or K″. The light receiving element 54 is arranged to tilt for the optical axis of the imaging lens 53 as shown in FIG. 20. The light receiving element 54 enables imaging in any position on the light receiving plane.
In this apparatus for measuring displacement, the irradiation point P moves in the direction of the height because of irregularities (displacement) on the surface of the measuring object 52 to be an irradiation point P′ or P″. Hereby, an image formation point K on the light receiving plane of the light receiving element 54 moves to the position of an image formation point K′ or K″. A signal from the light receiving element 54 also changes according to the amount of displacement of the image formation point K. The displacement in the height of the surface of the measuring object can be detected based upon the amount of the change of the signal.
The above mentioned apparatus for measuring displacement is provided with a mechanism for relatively displacing the measuring object 52 to the direction of the x-axis and the direction of the y-axis respectively orthogonal to the direction of the height. This mechanism is a low-speed mechanism normally driven by a motor and others. Therefore, when the measurement in minute pitch of the whole surface of the measuring object 52 is tried, it takes very long time.
Therefore, recently, the displacement of a measuring object 70 can be measured by only displacement in only the direction of the y-axis using scanning-type apparatus for measuring displacement 60 shown in FIG. 21. FIG. 21 is a schematic perspective view showing the scanning-type apparatus for measuring displacement 60.
A projecting system of the scanning-type apparatus for measuring displacement 60 is composed of a light source 61, a deflector 62 such as an oscillating mirror type and a convergent lens 63. Light radiated from the light source 61 is deflected in a range of fixed angles by the deflector 62. The deflected radiated light goes on one plane parallel with the optical axis of the convergent lens 63. The radiated light is incident on the surface 70a of the measuring object 70 set on a measuring table 71 at a predetermined angle of incidence. An irradiation point P formed by the radiated light is linearly scanned on both ways or on one way.
The radiated light is regularly reflected in the position of the irradiation point P on a light receiving system. An image of the irradiation point P is imagined on a light receiving plane 66a of a light receiving element 66 via a first cylindrical lens 64 and a second cylindrical lens 65. In this apparatus for measuring displacement 60, in case the reflectance of the surface 70a of the measuring object is high as that of a mirror, most of light reflected at the irradiation point P is incident on the light receiving system at the same angle as the angle of incidence based upon the irradiation point P.
However, in case the surface 70a of the measuring object is rough, the reflectance is low. In this case, the conventional scanning-type apparatus for measuring displacement 60 using the cylindrical lenses 64 and 65 for the light receiving system has a problem that when reflected light from the irradiation point P is scattered and is imaged on the light receiving plane 66a, an image on the light receiving plane is 66a of the light receiving element 66 becomes dim and the precision of measurement is remarkably deteriorated.
That is, the cylindrical lenses 64 and 65 basically show convergence in only the peripheral direction of the cylindrical face of each lens and have no convergence in other directions. Therefore, as shown in FIG. 22A, scattered light diffuse in the circumference of the cylindrical face of the first cylindrical lens 64 out of measuring beams reflected at the irradiation point P is converged by the first cylindrical lens 64 and is incident on the second cylindrical lens 65. The light is deflected by the second cylindrical lens 65 so that the light goes to the center of the light receiving plane 66a of the light receiving element 66 and forms an image formation point K on the light receiving plane 66a. 
Also, as shown in FIG. 22B, scattered light diffuse in the axial direction of the cylindrical face of the first cylindrical lens 64 out of menacing beams reflected at the irradiation point P is not converged by the first cylindrical lens 64 at all and is incident on the second cylindrical lens 65 in a state in which the light is diffuse. Therefore, an image formation point K on the light receiving plane 66a of the light receiving element 66 becomes a straight line extended in the width direction of the light receiving plane 66a. 
In addition, an image at the irradiation point P is converged by only the first cylindrical lens 64 the focal length of which is short. Therefore, an image K on the light receiving plane 66a of the light receiving element 66 is in the shape of arm ellipse long sideways because of the aberration of the first cylindrical lens 64 as shown in FIG. 23. Therefore, the image K in the shape of the ellipse long sideways cannot be made circular by converging it by the first cylindrical lens 64. Hereby, the variation of a signal output from the light receiving element 66 increases. Therefore, displacement on the measured surface cannot be measured at high precision.
Further, as shown in FIG. 24, the surface 70a of a measuring object 70 has irregularities and may have predetermined difference in a level 70b. In such a form, when light radiated from a projecting system is regularly reflected by a light receiving system, reflected light may be intercepted by this difference in a level 70b. In this case, displacement in the vicinity of a part having difference in a level 70b cannot be measured.